I just returned from the Camino a few days ago. I would definitely bring a sleeping bag. Most of the albergues, municipal and private have no heat. My bag is marmot, nanowave45, perfect weight. A few albergues provide disposable paper fitted sheet and pillow case. Some albergues do have clean fitted sheets for a couple of extra euros. Bringing along your own sheet would be ideal to put under your sleeping bag, however, due to weight restrictions that may not be practical. Also, washing and drying the sheet every other day would be a pain. The only albergue where the sheet was pretty disgusting was the public albergue in Ponferedda. I took the sheet off, washed it in the sink and dried it on the line in the sun before Putting my sleeping bag on it. A good idea is to bring a bandana which can be used as a pillow case, face cloth, hair band, hand towel (hang it on your pack while walking, not all bathrooms have towels.) Buen Camino! I wish I was still walking!
I did not encounter bed bugs, and heard no one else speaking about them. Some albergues do have extra blankets, I declined to use them for hygienic reasons. Yuck! I walked from Leon to Santiago.